Question: Simplify the following expression: $ a = \dfrac{2}{9} + \dfrac{p + 8}{p + 10} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{p + 10}{p + 10}$ $ \dfrac{2}{9} \times \dfrac{p + 10}{p + 10} = \dfrac{2p + 20}{9p + 90} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{p + 8}{p + 10} \times \dfrac{9}{9} = \dfrac{9p + 72}{9p + 90} $ Therefore $ a = \dfrac{2p + 20}{9p + 90} + \dfrac{9p + 72}{9p + 90} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{2p + 20 + 9p + 72}{9p + 90} $ $a = \dfrac{11p + 92}{9p + 90}$